Perhaps it's clear to you that no matter how your axes are oriented, when you ask, "How long is this arrow?"

这应该是比较显然的,无论坐标轴指向哪里,当你问,"这个矢量有多长"

耶鲁公开课 - 基础物理课程节选

So, there is a way to go from the unprimed coordinates to the prime coordinate by rotating your axis and actually calculating the components.

现在我们有一种方法可以从原坐标系,转变到新坐标系,只要旋转坐标轴,并实际地计算一下坐标即可

耶鲁公开课 - 基础物理课程节选

It dropped dramatically in the period from 1954-- this is these filled black bars refer to this axis, polio cases per 100,000 population dropped down to only three or four cases by 1956.

患病率在一九五四年后的,一段时间里急剧下降,该坐标轴上的这些黑色柱形图表明,到一九五六年,小儿麻痹症的发病率,已经降低至每十万人中仅三到四人发病

耶鲁公开课 - 生物医学工程探索课程节选

When you go from one set of axes to another set of axes, the numbers change.

当你将一组坐标轴变换到另一组坐标轴时,坐标值会发生变化

耶鲁公开课 - 基础物理课程节选

A magnitude is how long this guy is and direction is at what angle it is.

大小是指它的长度,而方向是指它与坐标轴的夹角

耶鲁公开课 - 基础物理课程节选

Actually, the view of vectors we take nowadays is that vectors are associated with a pair of numbers which, on the rotation of axes, transform like this.

实际上,今天我们讲矢量所用的观点是,矢量是和一组坐标值相对应的,在坐标轴旋转的过程中像这样变换

耶鲁公开课 - 基础物理课程节选

Pick any two perpendicular directions Then the same entity, the same arrow which has an existence of its own, independent of axis, can be described by you and me using different numbers.

选取两个互相垂直的方向,这样同样的物体,同一矢量,并且是独立于坐标轴而存在的,可以被你和我用不同的数字来描述

耶鲁公开课 - 基础物理课程节选